For many systems in science and engineering, the governing differential equation is either not known or known in an approximate sense. Analyses and design of such systems are governed by data collected from the field and/or laboratory experiments. This challenging scenario is further worsened when data-collection is expensive and time-consuming. To address this issue, this paper presents a novel multi-fidelity physics informed deep neural network (MF-PIDNN). The framework proposed is particularly suitable when the physics of the problem is known in an approximate sense (low-fidelity physics) and only a few high-fidelity data are available. MF-PIDNN blends physics informed and data-driven deep learning techniques by using the concept of transfer learning. The approximate governing equation is first used to train a low-fidelity physics informed deep neural network. This is followed by transfer learning where the low-fidelity model is updated by using the available high-fidelity data. MF-PIDNN is able to encode useful information on the physics of the problem from the {\it approximate} governing differential equation and hence, provides accurate prediction even in zones with no data. Additionally, no low-fidelity data is required for training this model. Applicability and utility of MF-PIDNN are illustrated in solving four benchmark reliability analysis problems. Case studies to illustrate interesting features of the proposed approach are also presented.

Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences, as the standard self-attention mechanism of the Transformer uses $O(n^2)$ time and space with respect to sequence length. In this paper, we demonstrate that the self-attention mechanism can be approximated by a low-rank matrix. We further exploit this finding to propose a new self-attention mechanism, which reduces the overall self-attention complexity from $O(n^2)$ to $O(n)$ in both time and space. The resulting linear transformer, the \textit{Linformer}, performs on par with standard Transformer models, while being much more memory- and time-efficient.

Clinical predictions using clinical data by computational methods are common in bioinformatics. However, clinical predictions using information from genomics datasets as well is not a frequently observed phenomenon in research. Precision medicine research requires information from all available datasets to provide intelligent clinical solutions. In this paper, we have attempted to create a prediction model which uses information from both clinical and genomics datasets. We have demonstrated multiclass disease predictions based on combined clinical and genomics datasets using machine learning methods. We have created an integrated dataset, using a clinical (ClinVar) and a genomics (gene expression) dataset, and trained it using instance-based learner to predict clinical diseases. We have used an innovative but simple way for multiclass classification, where the number of output classes is as high as 75. We have used Principal Component Analysis for feature selection. The classifier predicted diseases with 73\% accuracy on the integrated dataset. The results were consistent and competent when compared with other classification models. The results show that genomics information can be reliably included in datasets for clinical predictions and it can prove to be valuable in clinical diagnostics and precision medicine.

This work studies the robust subspace tracking (ST) problem. Robust ST can be simply understood as a (slow) time-varying subspace extension of robust PCA. It assumes that the true data lies in a low-dimensional subspace that is either fixed or changes slowly with time. The goal is to track the changing subspaces over time in the presence of additive sparse outliers and to do this quickly (with a short delay). We introduce a ``fast'' mini-batch robust ST solution that is provably correct under mild assumptions. Here ``fast'' means two things: (i) the subspace changes can be detected and the subspaces can be tracked with near-optimal delay, and (ii) the time complexity of doing this is the same as that of simple (non-robust) PCA. Our main result assumes piecewise constant subspaces (needed for identifiability), but we also provide a corollary for the case when there is a little change at each time. A second contribution is a novel non-asymptotic guarantee for PCA in linearly data-dependent noise. An important setting where this result is useful is for linearly data-dependent noise that is sparse with enough support changes over time. The subspace update step of our proposed robust ST solution uses this result.

We provide a comprehensive analysis of the Stochastic Heavy Ball (SHB) method (otherwise known as the momentum method), including a convergence of the last iterate of SHB, establishing a faster rate of convergence than existing bounds on the last iterate of Stochastic Gradient Descent (SGD) in the convex setting. Our analysis shows that unlike SGD, no final iterate averaging is necessary with the SHB method. We detail new iteration dependent step sizes (learning rates) and momentum parameters for the SHB that result in this fast convergence. Moreover, assuming only smoothness and convexity, we prove that the iterates of SHB converge \textit{almost surely} to a minimizer, and that the convergence of the function values of (S)HB is asymptotically faster than that of (S)GD in the overparametrized and in the deterministic settings. Our analysis is general, in that it includes all forms of mini-batching and non-uniform samplings as a special case, using an arbitrary sampling framework. Furthermore, our analysis does not rely on the bounded gradient assumptions. Instead, it only relies on smoothness, which is an assumption that can be more readily verified. Finally, we present extensive numerical experiments that show that our theoretically motivated parameter settings give a statistically significant faster convergence across a diverse collection of datasets.

Learning to follow instructions is of fundamental importance to autonomous agents for vision-and-language navigation (VLN). In this paper, we study how an agent can navigate long paths when learning from a corpus that consists of shorter ones. We show that existing state-of-the-art agents do not generalize well. To this end, we propose BabyWalk, a new VLN agent that is learned to navigate by decomposing long instructions into shorter ones (BabySteps) and completing them sequentially. A special design memory buffer is used by the agent to turn its past experiences into contexts for future steps. The learning process is composed of two phases. In the first phase, the agent uses imitation learning from demonstration to accomplish BabySteps. In the second phase, the agent uses curriculum-based reinforcement learning to maximize rewards on navigation tasks with increasingly longer instructions. We create two new benchmark datasets (of long navigation tasks) and use them in conjunction with existing ones to examine BabyWalk's generalization ability. Empirical results show that BabyWalk achieves state-of-the-art results on several metrics, in particular, is able to follow long instructions better. The codes and the datasets are released on our project page https://github.com/Sha-Lab/babywalk.

A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is proportional to the fraction of issues, where his preferences disagree with the decision. While an issue-by-issue vote by all voters would maximize social welfare, we are interested in how well the preferences of the population can be approximated by a small committee. We show that a k-sortition (a random committee of k voters with the majority vote within the committee) leads to an outcome within the factor 1+O(1/k) of the optimal social cost for any number of voters n, any number of issues $m$, and any preference profile. For a small number of issues m, the social cost can be made even closer to optimal by delegation procedures that weigh committee members according to their number of followers. However, for large m, we demonstrate that the k-sortition is the worst-case optimal rule within a broad family of committee-based rules that take into account metric information about the preference profile of the whole population.

Drawing on the idea that brain development is a Darwinian process of ``evolution + selection'' and the idea that the current state is a local equilibrium state of many bodies with self-organization and evolution processes driven by the temperature and gravity in our universe, in this work, we describe an artificial intelligence system called the ``Synergetic Learning Systems''. The system is composed of two or more subsystems (models, agents or virtual bodies), and it is an open complex giant system. Inspired by natural intelligence, the system achieves intelligent information processing and decision-making in a given environment through cooperative/competitive synergetic learning. The intelligence evolved by the natural law of ``it is not the strongest of the species that survives, but the one most responsive to change,'' while an artificial intelligence system should adopt the law of ``human selection'' in the evolution process. Therefore, we expect that the proposed system architecture can also be adapted in human-machine synergy or multi-agent synergetic systems. It is also expected that under our design criteria, the proposed system will eventually achieve artificial general intelligence through long term coevolution.

Morpion Solitaire is a popular single player game, performed with paper and pencil. Due to its large state space (on the order of the game of Go) traditional search algorithms, such as MCTS, have not been able to find good solutions. A later algorithm, Nested Rollout Policy Adaptation, was able to find a new record of 82 steps, albeit with large computational resources. After achieving this record, to the best of our knowledge, there has been no further progress reported, for about a decade. In this paper we take the recent impressive performance of deep self-learning reinforcement learning approaches from AlphaGo/AlphaZero as inspiration to design a searcher for Morpion Solitaire. A challenge of Morpion Solitaire is that the state space is sparse, there are few win/loss signals. Instead, we use an approach known as ranked reward to create a reinforcement learning self-play framework for Morpion Solitaire. This enables us to find medium-quality solutions with reasonable computational effort. Our record is a 67 steps solution, which is very close to the human best (68) without any other adaptation to the problem than using ranked reward. We list many further avenues for potential improvement.

We study the problem of modeling purchase of multiple items and utilizing it to display optimized recommendations, which is a central problem for online e-commerce platforms. Rich personalized modeling of users and fast computation of optimal products to display given these models can lead to significantly higher revenues and simultaneously enhance the end user experience. We present a parsimonious multi-purchase family of choice models called the BundleMVL-K family, and develop a binary search based iterative strategy that efficiently computes optimized recommendations for this model. This is one of the first attempts at operationalizing multi-purchase class of choice models. We characterize structural properties of the optimal solution, which allow one to decide if a product is part of the optimal assortment in constant time, reducing the size of the instance that needs to be solved computationally. We also establish the hardness of computing optimal recommendation sets. We show one of the first quantitative links between modeling multiple purchase behavior and revenue gains. The efficacy of our modeling and optimization techniques compared to competing solutions is shown using several real world datasets on multiple metrics such as model fitness, expected revenue gains and run-time reductions. The benefit of taking multiple purchases into account is observed to be $6-8\%$ in relative terms for the Ta Feng and UCI shopping datasets when compared to the MNL model for instances with $\sim 1500$ products. Additionally, across $8$ real world datasets, the test log-likelihood fits of our models are on average $17\%$ better in relative terms. The simplicity of our models and the iterative nature of our optimization technique allows practitioners meet stringent computational constraints while increasing their revenues in practical recommendation applications at scale.